Existence and regularity of inverse problem for the nonlinear fractional Rayleigh‐Stokes equations

Abstract

This paper investigates an inverse problem for fractional Rayleigh‐Stokes equations with nonlinear source. The fractional derivative in time is taken in the sense of Riemann‐Liouville. The proposed problem has many applications in some non‐Newtonian fluids. We obtain some results on the existence and regularity of mild solutions.

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

“…Regarding analytic representation for solution of this problem in linear form, we refer to [7,8,13,15,17,18]. Recently, the final value problem involving (1) has been addressed in [9,10,14], as an interesting supplement to qualitative investigation for this equation.…”

On Ulam–Hyers–Rassias stability of a generalized Caputo type multi-order boundary value problem with four-point mixed integro-derivative conditions

“…For the sake of simplicity in writing, we take κ ϕ = W 2 + 1. Then (19) becomes v(t)u(t) ≤ κ ϕ εϕ(t).…”

“…(for example, refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Many researchers play an important role in different desirable developments on the existence criteria, and some results about the uniqueness for numerous fractional differential equations have been obtained (see for instance [7,[16][17][18][19][20][21][22][23][24]). On the other hand, the subject of stability is a very important notion in physics since most phenomena in the real world include this concept.…”

A nonlinear fractional Rayleigh–Stokes equation under nonlocal integral conditions

“…The backward problems have currently been studied by many mathematicians. Ngoc et al [24], for instance, pondered the inverse problem for the nonlinear fractional Rayleigh-Stokes equations. Equation (1.1) associated with Gaussian random noise was examined by Triet et al [25], and so forth.…”